Patterns » Dragon Curve Fractal Hat

  • Dragon Curve Fractal Hat

Knit this beautiful reversible fractal hat to show your love of mathematical art!

Fractals have always fascinated me. They are a beautiful combination of mathematics and art. At its most basic level, a fractal is a pattern that looks similar at every level of magnification. The Dragon Curve Fractal is the fractal featured in the chapter headings for Jurassic Park by Michael Crichton.

The Dragon Curve Fractal is created by applying a transformation to a line multiple times as follows:

I designed this hat to show off the lacy design of the Dragon Curve Fractal. It is a medium weight, double knit hat that features this fractal repeated all around the hat. Contrasting yarns show off the design, especially if one of the yarns is a variegated yarn. The hat is fully reversible, featuring opposite color schemes on each side. Try wearing the hat with the matching Dragon Curve Fractal Scarf.

Full instructions are included for the double knitting technique. This hat will fit an average adult. It is possible to increase the size a little by using a larger needle size, depending on your gauge. The color work design is chart only, not written instructions.


  • 160-180 yards each of two contrasting colors of fingering weight yarn.
  • Size 1 US (2.25 mm) needles.
  • Cable needle or spare needle to hold a stitch for increases and decreases.
  • 10 stitch markers, one of which must be distinct to indicate the end of a round.
  • Needle to weave in ends.

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